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Abstract

Disclosed is an algorithm for determining the order of autoregressive (AR) models based on the Predictive Least-Squares principle. The implementation of the order-determining algorithm uses predictive lattice filters, also called ladder forms, that have a modular structure amenable to VLSI implementation. AR models are used in speech modelling and synthesis, equalization of communication channels, spectral estimation, time series analysis and other areas. Given a sequence of t observations of y, we can predict the next observation t+1 of y using a so-called all-pole autoregressive (AR) model of order m as set out in equation (1), (Image Omitted) where the number m and the coefficients a are to be estimated from the t observations of y.

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United States

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English (United States)

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Order Selection for AR Models by Predictive Least Squares

Disclosed is an algorithm for determining the order of autoregressive (AR)
models based on the Predictive Least-Squares principle. The implementation of
the order-determining algorithm uses predictive lattice filters, also called ladder
forms, that have a modular structure amenable to VLSI implementation. AR
models are used in speech modelling and synthesis, equalization of
communication channels, spectral estimation, time series analysis and other
areas. Given a sequence of t observations of y, we can predict the next
observation t+1 of y using a so-called all-pole autoregressive (AR) model of order
m as set out in equation (1),

(Image Omitted)

where the number m and the coefficients a are to be estimated from the t
observations of y. In particular, for a fixed order m the least squares estimates of
the coefficients are given by the well-known formula set out in equation (2),

(Image Omitted)

where the matrices Y(t), Y'(t) are defined by the observed data. After having
observed T data points, we can estimate an optimal order m by minimizing the
accumulated prediction errors as set out in equation (3).

(Image Omitted)

To find this estimate requires the computation of the estimated coefficients
according to equation (2), T times for each selected value of m until the minimum
is found. But the sum of prediction errors (equation 3) can be calculated without
specifically computing the coefficient estimates (equ...